What is the antiderivative of e^2x? I know the antiderivative of e^x is e^x. Would e^2x's antiderivative still be e^2x??
You want F(x) such that F'(x)=e^2x
Try F = (1/2)e^2x + C
=(e^2x)/2
=(e^2x)/2
what is the anti derivative of
70e^-.6t
70/-.6 times e^.6t
wouldnt it be 70/-.6 times e^-.6t?
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the answer is 7
To find the antiderivative of e^2x, you can use the power rule of integration.
The power rule states that if you have an expression of the form x^n, where n is a constant (not equal to -1), the antiderivative is (1/(n+1))x^(n+1) + C, where C is the constant of integration.
In this case, you have e^2x, where the exponent is 2x. To apply the power rule, let's rewrite it as (e^2)^x.
Since the base is a constant (e^2), you can treat it as a constant term. Applying the power rule, you would integrate (e^2)^x as (1/(2+1))(e^2)^x + C, which simplifies to (1/3)(e^2x) + C.
So, the antiderivative of e^2x is (1/3)(e^2x) + C, where C is the constant of integration.